Digital transmission method of the error correcting coding type

ABSTRACT

A digital transmission method of the error correcting coding type comprises a coding procedure before transmission and a decoding procedure in order to obtain a correction of the transmission errors. The said coding procedure comprises a plurality of elementary coding steps associated in parallel or in series. The decoding procedure is iterative and comprises, for each iteration, a plurality of elementary decoding steps ( 50 ) which correspond to the said plurality of elementary coding steps and which each generate at least one extrinsic information item. According to the invention a characteristic quantity determination step ( 51 ) calculates a characteristic quantity from a set of weighted output information,on items generated by an elementary decoding step ( 50 ) for processing a decoding sequence. A comparison step ( 53 ) is adapted to compare the said characteristic quantity with a threshold quantity determined by a threshold quantity determination step ( 52 ). An interrupt step ( 54 ) interrupts the said decoding procedure at an elementary decoding step ( 50 ) for which the said characteristic quantity attains the said threshold quantity.  
     Advantageously, the said threshold quantity determination step ( 52 ) determines a threshold quantity so as to effect a compromise between the performance permitted by the said decoding procedure and the complexity of this decoding procedure. Likewise, the said threshold quantity determination step ( 52 ) can determine a threshold quantity as a function of a required mean transmission time or as a function of an acceptable mean energy consumption.

[0001] The present invention concerns in general terms a digitaltransmission method of the error correcting coding type, notably for asystem for digital transmission over a channel with a large amount ofinterference. More precisely, it concerns the interruption of theiterative decoding of a digital transmission method of the errorcorrecting coding type using coding schemes of the turbocode type.

[0002] A digital transmission system conveys information using aphysical carrier such as cable, optical fibre or propagation on a radiochannel, satellite or otherwise. Such a physical medium will be referredto as a channel. Generally, such a system comprises in particular, onthe sending side, a device referred to as a channel coder and, on thereceiving side, a corresponding decoding device.

[0003] The channel coding device has a so-called error correcting codingfunction. The error correcting coding function consists of generatingredundant information on sending which, during decoding at thedestination, will make it possible to reconstitute the usefulinformation transmitted, using the information arriving at itsdestination, referred to as the received information, affected by thedisturbance occurring on the channel, notably of the noise, attenuationand interference type. A digital transmission method using such achannel coding associated with a corresponding destination decoding isreferred to as a transmission method of the error correcting codingtype.

[0004] For example, the coding operation takes place at the level of thebit. This operation associates with a binary sequence of usefulinformation a binary sequence of corresponding coded information. Thisbinary sequence of coded information is referred to as the code wordwhen the size of the binary sequences of useful information is fixed.The binary sequence of coded information is of greater size than thebinary sequence of useful information so as to introduce redundancy.Because of this redundancy, only certain coded information sequences, inaccordance with the coding law, are possible. If received informationsequences to be decoded are different from these possible sequences, itis because they correspond to information impaired by the channel. Therole of the decoding method will therefore be to reconstitute the usefulinformation as well as possible from the received information sequence,knowing the coding law used. It is known how to decode the most simplecodes in optimum fashion, that is to say by finding, amongst thepossible sequences, the most likely sequence. For the more complex codessuch as turbocode, the limiting factor is in general the complexity ofthe decoder.

[0005] The performance of a transmission with error correcting coding isgenerally measured in terms of rate of binary errors or packets for agiven signal to noise ratio E_(b)/N_(o), where E_(b) is the energy perinformation bit and N_(o) is the power spectral density of the noise. Acode is referred to as more or less efficient depending on whether itsuse affords a higher or lower error rate for a given ratio E_(b)/N_(o)and for a given decoding complexity.

[0006] The efficiency of the code is the number of useful informationbits per coded information bit.

[0007] Known error correcting codes are block codes. Block codingconsists of associating with each block of k information bits a block ofn bits (n>k) therefore containing (n-k) redundant bits. The block of nbits is obtained by multiplying the block of k useful bits by a matrixwith k rows and n columns referred to as a generating matrix for thecode. When, by permutation, the generating matrix is written in a formsuch that it reveals the identity matrix, so that, in the block of nbits, the k information bits and the n-k redundancy bits are separated,the code is said to be systematic. The efficiency of the code is equalto k/n. The decoding device detects the errors and corrects them bymeans of the minimum Hamming distance. Such error correcting codes wellknown in the art are for example Hamming codes, BCH codes andReed-Solomon codes.

[0008] Effecting an error correcting coding by means of one or moreconvolutional codings is also well known. Their operating principleconsists of coding a block of k binary elements present at the input ofthe coder as a block of n binary elements also taking account of mblocks preceding the block present in the input, using a device with aregister of the shift register type. The output of the convolutionalcoder consists of n coded binary elements generated by the convolutionproduct of the k binary elements present at the input with the responseof the coder defined by n generator polynomials. The efficiency of thecode is equal to k/n. The decoding device reconstructs the originaldata, for example by means of a decoding of the sequential type, adecoding according to the most likely symbol, or a decoding according tothe most likely sequence, as described, for example, in the document“Digital Communications”, by J. G. Proakis, which appeared in 1995 in apublication by MacGraw-Hill. For example, the Viterbi algorithm providesan optimum decoding according to the most likely sequence.

[0009] According to a variant of this type of code, coding is noteffected by directly taking into account a series of m usefulinformation items preceding the information to be coded, but by using aseries of m auxiliary information items, stored in a device of the shiftregister type, each obtained by the mathematical combination of a usefulinformation item and m auxiliary information items calculatedpreviously. Such a convolutional code is said to be recursive. When, inaddition, the useful information appears as it is amongst the n outputsof the coder alongside (n−1) coded information items or redundantinformation items, the resulting code is referred to as a recursivesystematic convolutional code, or RSC code.

[0010] Associating different coders in order to increase the performanceof the coding is also known. For example, the data coded by a firstcoder can supply a second coder. Decoding takes place symmetrically,commencing with the second code.

[0011] A high-performance type of combination of coders has beenproposed, as described notably in the document “Near Shannon LimitError-Correcting Coding and Decoding: Turbo-codes” by C. Berrou, A.Glavieux and P. Thitimajshima, which appeared in ICC-1993, ConferenceProceedings, on pages 1064-1070. This type of combination of coders hasgiven rise to a family of coding schemes known in the art as turbocodes.The term turbocodes will be given to error correcting codes based on thecombination, referred to as concatenation, of several simple codes,referred to as elementary codes, with the intervention of permutationoperations, referred to as interleavings, which modify the order oftaking into account of the data by each of the simple codes. Forexample, one type of conventional interleaving, referred to as uniforminterleaving, is obtained by means of an interleaving matrix in whichthe source data are introduced row by row and retrieved column bycolumn. In general, in order to improve the performance, the turbocodesuse non-uniform interleavings. Elementary codes means codes with anefficiency greater than or equal to 1, of the type described above. Itmay, for example, be a case of recursive systematic convolutional codesfor convolutional turbocodes, Hamming block codes or BCH for blockturbocodes. Different types of concatenation can be envisaged. Inparallel concatenation, the same information is coded for each coderseparately after having been interleaved. In serial concatenation, theoutput of each coder is coded by the following coder after having beeninterleaved. The term dimension of the turbocode refers to the number ofelementary coders used for implementing this turbocode. A well knownturbocoding scheme consists of a parallel concatenation of elementarycodes of the recursive systematic convolutional (RSC) code type. Thisturbocode is referred to by the term PCCC. Examples of turbocodes withserial concatenation are SCCCs which use elementary codes of theconvolutional code type and block turbocodes which use elementary codesof the block code type.

[0012] Information coded by a turbocode can be decoded by an iterativemethod referred to as turbodecoding. An example of turbodecoding isgiven in the aforementioned document “Near Shannon LimitError-Correcting Coding and Decoding: Turbo-codes”, by C. Berrou, A.Glavieux and P. Thitimajshima, which appeared in ICC-1993, ConferenceProceedings, on pages 1064-1070. In this example, it is a case of theturbodecoding of a turbocode with parallel concatenation. There arecombined several elementary decoders with weighted inputs and outputseach corresponding to an elementary coder of the coding device. Theweighted inputs and outputs are effected in terms of probabilities,likelihood ratios or log likelihood ratios. The weighted inputs andoutputs are generally associated with each of the mary symbols at theinput and output of the elementary coders, that is to say, for example,with bits if binary coders are used as elementary coders. The decoderswork one after the other in the case of a type of turbodecoding referredto as serial turbodecoding, or simultaneously in a type of turbodecodingknown as parallel turbodecoding. Intermediate concatenation schemes canalso be envisaged. Interleavers and deinterleavers act as a function ofthe interleavings carried out at coding. They enable each decoder totake into account an information item which is presented in the sameorder as at the output and input of the corresponding coder. Eachelementary decoder uses the available information which corresponds tothe information at the input and output of the corresponding elementarycoder. The available information used by the elementary decoder,referred to as a priori information, consists of an output of the steppreceding the channel decoding, namely, in general, a demodulation step,and an information item generated by one or more previous elementarydecoding steps. By virtue of this a priori information and knowing thecoding law of the corresponding elementary coder, the elementary decodergenerates an a posteriori information item which is an estimation of thegreatest reliability of the input information. The additionalinformation compared with the input information is referred to asextrinsic information. This extrinsic information is transmitted to thefollowing elementary decoder, which will use it as a priori informationafter interleaving or deinterleaving, and possible combination. Eachelementary decoding step therefore benefits at the input from a prioriinformation whose quality is increased by the elementary decodingscarried out during the previous elementary decoding steps. Thisextrinsic information depends on the redundant information introduced bythe corresponding coder. The method is iterative in that the extrinsicinformation calculated by the last decoder or decoders in the series ispropagated back to the first decoder or decoders in the series. Theexchange of extrinsic information takes place between elementarydecoders within the same step, and from this step to the following step.Each new step therefore increases the reliability of the informationgenerated at an output. After a certain number of iterations, thedecoding process stagnates, whether or not it has converged towards thesolution. A thresholding is applied in order to generate the decodedinformation.

[0013] Naturally, the term turbodecoding encompasses variousconcatenation schemes which can be envisaged, depending for example onthe type of turbocoding implemented. For example, in the turbodecodingcorresponding to a turbocode with serial concatenation, the elementarydecoders being associated in the reverse order of the elementary coders,each elementary decoder receives two a priori weighted information itemscorresponding one to the output information from the correspondingelementary coder and the other to the input information of thecorresponding elementary coder. This elementary decoder produces two aposteriori weighted information items, one corresponding to the outputof the corresponding elementary coder, and which therefore becomes, atthe time of a following iteration, after corresponding interleaving, thea priori input of a preceding elementary decoder, and the othercorresponding to the input of the corresponding elementary coder, whichtherefore becomes, in the same iteration, after correspondingdeinterleaving, the a priori input of a following elementary decoder.

[0014] Whatever the case, the extrinsic information can always bedefined as the additional information given by an elementary decodingassociated with an elementary coding with respect to an a prioriinformation item, acting at the input of the elementary decoding.

[0015] In addition, it is possible to use various types of algorithm forelementary decoders with weighted inputs and outputs. Elementarydecoders use, for example, MAP, LogMAP and MaxLogMAP algorithms, alsoreferred to as APP, LogAPP and MaxLogAPP, which all derive from thecalculation of a posteriori probabilities knowing a prioriprobabilities. Reference can be made, for a description of such decodingalgorithms, for example, to the article “Optimal and sub-optimal maximuma posteriori algorithms suitable for turbo decoding” by P. Robertson, P.Hoeher and E. Villebrun, which appeared in European Trans. onTelecommun., vol. 8, March-April 1997, pages 119-125. It is alsopossible to use algorithms of the Viterbi algorithm type modified toassociate, with each decision, a reliability measurement of a typecomparable to LLR (log likelihood ratio). It is, for example, possibleto use the SOVA (Soft Output Viterbi Algorithm). For block turbocodes,it is possible to use a Chase algorithm, as described in the article “Avery low complexity block turbo decoder for product codes” by R.Pyndiah, P. Combelles and P. Adde, which appeared in IEEE Globecom 1996,pages 101 to 105.

[0016] It is also known that the efficiency of a code can be increasedby a puncturing operation which consists of transmitting only certainbits of an information sequence, as described, for example, in thearticle “Rate-Compatible Punctured Convolutional (RCPC) codes and theirapplication”, by J. Hagenauer, which appeared in IEEE Trans., VolCOM-36.4, 1988, pages 389-400 or in the article “New Rate CompatiblePunctured Convolutional Codes for Viterbi Decoding”, by L. H. C. Lee,which appeared in IEEE Trans., Vol. COM-42.2, 1994, pages 3073-3079.These non-transmitted bits are in general redundant information bits.This puncturing operation occurs at the sending level, after the codingoperation. At the destination, a reciprocal operation of depuncturing iscarried out before the decoding operation. The puncturing anddepuncturing operations are defined by a puncturing matrix or diagram.The puncturing of redundant information bits reduces the correctioncapability of the code and increases its efficiency.

[0017] The error correcting codes of the family of turbocodes accordingto the state of the art described above make it possible to obtain avery high performance error correction whilst preserving sufficientlyhigh efficiencies and allowing decoding operations of low complexitycompared with the complexity of the code. Turbodecoding, sub-optimal inits principle, has a performance close to that of the optimal decoderand an appreciably lower complexity, since it is of the order of that ofthe decoding of the elementary codes.

[0018] However, the complexity of the turbodecoding and parameters suchas the turbodecoding time or the energy consumption for turbodecodingcan increase with a number of iterations of the turbodecoding procedure.There is then posed the problem of interruption of the turbodecoding.Naturally, a predetermined number of turbodecoding iterations can befixed. However, it may happen then that this predetermined number ofiterations is either insufficient, then not making it possible toachieve a satisfactory error correction, or too high, meaning that acertain number of iterations are unnecessary. This way of proceedingthen takes place either to the detriment of the transmissionperformance, measured for example in terms of bit error rate, or to thedetriment of the transmission conditions such as the complexity of theturbodecoding, the turbodecoding time or the consumption of energy forturbodecoding.

[0019] Generally, a maximum number of iterations is fixed correspondingto an acceptable complexity and/or maximum decoding time, and a stopcriterion is used for interrupting the decoding process if this seems tohave given rise to a convergence towards the useful information beforethe maximum number of iterations Convergence can be detected indifferent ways. For example, an error detection code of the CRC (CyclicRedundancy Check) type may be used. If, during the decoding of aninformation sequence, the calculation of the error detecting codeindicates that there are no more errors, the iterative decoding for thesequence is interrupted. A drawback of this method stems from the factthat an error detecting code must be introduced on transmission, whichreduces the overall efficiency of the channel coder.

[0020] There have also been proposed criteria for the interruption ofthe turbodecoding based on a comparison of information sequences at theoutput of at least two successive elementary decoders. Such interruptioncriteria are described, for example, in an article by M. Moher whosetitle is “Decoding via Cross-Entropy Minimization”, which appeared in“Proceedings of Globecom '93, IEEE Global TelecommunicationsConference”, vol. 2, pages 809-813, or in an article by R. Y. Shao, S.Lin and M. P. C. Fossorier entitled “Two simple stopping criteria forturbo-decoding”, which appeared in “IEEE Transactions on Comm.”, vol 47,n°8, August 1999, pages 1117-1120. The use of such criteria forinterruption of the turbodecoding is based notably on the fact that astagnation of the outputs of the elementary decoders during theiterative decoding of a sequence of information indicates thatadditional decoding iterations will not further reduce the number oferrors occurring on this information sequence.

[0021] Nevertheless, this type of turbodecoding interruption criterionposes two types of problem.

[0022] First of all, though the principle on which this criterion isbased makes it possible, in a relatively simple manner, to control thestoppage of the decoding processing, it does not give any indication ofthe quality of the decoded information sequences, that is to say on thenumber of errors which they contain with respect to the usefulinformation nor even on the possible presence of residual errors.

[0023] Next, the use of this type of interruption criterion assumes thestorage of an information sequence issuing from a step which precedesthe decoding step under consideration in order to carry out thecomparison. Generally, it is even necessary to store several sequencesissuing from steps preceding the step under consideration so that thefunctioning of the criterion is satisfactory.

[0024] Finally, since this interruption criterion is based on astagnation of the outputs of successive elementary decoders, it detectsthe convergence of the decoding method at least one step after it haseffectively converged. In the case of a convergence at the penultimatestep of elementary decoding, the last step effected is thereforeunnecessary.

[0025] One object of the present invention is therefore to improve theinterruption of the iterative decoding of a digital transmission methodof the type with error correcting coding using coding schemes of theturbocode type. For this purpose, a criterion of interruption of theturbodecoding making it possible to resolve the problems mentioned abovehas been sought.

[0026] To this end, it proposes a digital transmission method of thetype with error correcting coding, comprising, before a step oftransmission over a channel, a coding procedure for generating, from auseful information item, a coded information item comprising at leastone redundant information item and, after the said step of transmissionover the said channel, a decoding procedure in order to obtain, from areceived information item to be decoded, an estimation of said usefulinformation item with correction of the transmission errors based onsaid at least one redundant information item, said coding procedurecomprising a plurality of elementary coding steps associated with atleast one interleaving step and operating in parallel or in series, saiddecoding procedure being iterative and comprising, for each iteration, aplurality of elementary decoding steps associated with interleaving anddeinterleaving steps, corresponding to said plurality of elementarycoding steps associated with said at least one interleaving step, eachof said elementary decoding steps receiving a set of information to bedecoded and generating a set of weighted output information itemnsassociated with a set of decoded information, the said method beingcharacterised in that it comprises a step of determining acharacteristic quantity adapted to calculate, for each of saidelementary decoding steps, a quantity characteristic of the said set ofweighted output information items, a comparison step adapted to comparethe said characteristic quantity with a threshold quantity, and aninterrupt step for interrupting said decoding procedure when saidcharacteristic quality reaches the said threshold quantity.

[0027] Advantageously, the said characteristic quantity determinationstep is adapted to calculate, for each of the said elementary decodingsteps, a quantity characteristic of a set of extrinsic information itemscorresponding to said set of weighted output information itemsassociated with a set of decoded information.

[0028] It is in fact advantageous to calculate this characteristicquantity from the extrinsic information which makes it possible to givein a simple manner an indication of the number of errors remaining in adecoding sequence.

[0029] It will be understood that it is nevertheless possible tocalculate a characteristic quantity directly from the weighted outputsin which, after a certain number of iterations, the extrinsicinformation becomes essential.

[0030] It has been determined that there exists a correlation between onthe one hand the mean of the absolute value of the extrinsic informationcalculated on a sequence of N extrinsic values at the output of a givendecoder during a given iteration, and on the other hand a number oferrors remaining in the sequence of N decoded bits at the output of agiven decoder for this given iteration. It is found that this meanincreases rapidly as soon as the decoding of the sequence convergeswhilst it stagnates as long as this decoding does not converge. Thus,when this mean reaches a sufficient threshold quantity, there exists ahigh probability that the sequence does not contain any errors. Ittherefore becomes unnecessary to continue the decoding of this sequence.

[0031] It has been possible to establish curves, such as the onedepicted in FIG. 3, showing, for different transmission conditions,expressed for example in terms of signal to noise ratio, the differencebetween the mean of the absolute value of the extrinsic information forbadly decoded sequences and correctly decoded sequences.

[0032] Thus, advantageously, the characteristic quantity calculated bythe said characteristic quantity determination step will be the mean ofthe absolute value of the extrinsic information item calculated on allthe extrinsic information items considered. In this case, the interruptstep will interrupt the decoding procedure when the mean of the absolutevalue of the extrinsic information calculated by the characteristicquantity determination step is greater than an adapted thresholdquantity.

[0033] However, this characteristic quantity can also be anotherstatistical quantity characteristic of this set of extrinsic informationitems, such as its variance, its minimum or its maximum. It is alsopossible to use the sum of the absolute values of the extrinsicinformation items of this set of extrinsic information items.

[0034] Thus defined, the present invention applies to all types oftransmission method using an error correcting coding of the turbocodingtype and turbodecoding, whether it is a case of a turbocoding withserial or parallel concatenation, a turbodecoding with serial orparallel concatenation or mixed concatenation schemes.

[0035] According to another aspect of the present invention, the digitaltransmission method also comprises a threshold quantity determinationstep for determining a threshold quantity as a function of at least oneconfiguration parameter.

[0036] A configuration parameter can be a parameter characterising thetransmission conditions such as, for example, the signal to noise ratio.It can also be a case of a parameter characterising, for example, anelementary decoding algorithm, the size of the block of usefulinformation, a type of quantities used, a maximum number of iterations,a type of transmission channel, etc. Naturally, in general, thethreshold quantity determination step will determine a thresholdquantity as a function of a plurality of configuration parameters.

[0037] This threshold quantity determination step can use an adaptivealgorithm allowing the calculation of a threshold quantity as a functionof one or more configuration parameters.

[0038] This threshold quantity determination step can also usepre-established reference tables making it possible to select athreshold quantity as a function of one or more configurationparameters.

[0039] According to another aspect of the present invention, the saidthreshold quantity determination step determines a threshold quantity soas to effect a compromise between the permitted performance for the saiddecoding procedure and the complexity of this decoding procedure.

[0040] For example, where the characteristic quantity chosen is the meanof the absolute value of the extrinsic information, the thresholdquantity will be chosen on the one hand so as to be sufficiently largeto ensure that the number of errors remaining in a decoded sequence issufficiently low and on the other hand sufficiently small to limit thenumber of iterations necessary to achieve this threshold value.

[0041] In a similar manner, the said threshold quantity determinationstep determines a threshold quantity so as to ensure a certain qualityof transmission.

[0042] For example, the said threshold quantity determination stepdetermines a threshold quantity as a function of a mean transmissiontime required.

[0043] The said threshold quantity determination step can also determinea threshold quantity as a function of an acceptable mean energyconsumption.

[0044] According to another aspect of the present invention, a maximumtolerable number of iterations having been predefined, the saidthreshold quantity determination step determines a threshold quantity bycombining on the one hand a first quantity characteristic of a first setof extrinsic information generated by a last elementary decoder during alast iteration and associated with a first set of decoded informationcorresponding to the error-free decoding of a set of information to bedecoded, and on the other hand a second quantity characteristic of asecond set of extrinsic information generated by the said last decoderduring the said last iteration and associated with a second set ofdecoded information corresponding to the decoding of the said set ofinformation to be decoded in a case where errors remain.

[0045] Advantageously, the said first and second quantities will be themeans of the absolute value of the extrinsic information calculated on,respectively, the said first set of extrinsic information and the saidsecond set of extrinsic information.

[0046] However, these first and second quantities can also be any otherstatistical quantities characteristic of respectively these first andsecond sets of extrinsic information, such as their variances, theirminima or their maxima. It is also possible to use the sums of theabsolute values of the extrinsic information of, respectively, thesefirst and second sets of extrinsic information.

[0047] The said first and second quantities can be determined, as afunction of at least one configuration parameter, by means of anadaptive algorithm or a pre-established reference table. In practice,these first and second quantities will be established as a function of aplurality of configuration parameters.

[0048] The said threshold quantity can notably be the sum of the saidfirst quantity multiplied by a coefficient α and the said secondquantity multiplied by a coefficient (1-α), the coefficient α beingchosen so as to be between 0 and 1.

[0049] Advantageously, this coefficient α will be chosen so as to effecta compromise between the performance permitted for the said decodingprocedure and the complexity of this decoding procedure.

[0050] For example, where the characteristic quantity chosen is the meanof the absolute value of the extrinsic information, the coefficient αwill be chosen on the one hand so as to be sufficiently large to ensurethat the number of errors remaining in a decoded sequence issufficiently low and on the other hand sufficiently low to limit thenumber of iterations performed by the decoding procedure.

[0051] In a similar maimer, the coefficient α will be chosen so as toensure a certain transmission quality.

[0052] For example, the coefficient α will be chosen as a function of amean required transmission time.

[0053] The said coefficient α can also be chosen as a function of anacceptable mean energy consumption.

[0054] Advantageously, the coefficient α is determined by means of anadaptive algorithm or a pre-established reference table.

[0055] According to another aspect of the present invention, the saidelementary decoding steps have inputs and outputs which are weighted, interms of probabilities, likelihood ratios, or log likelihood ratios.

[0056] According to another aspect of the present invention, the saidcoding procedure comprises at least one puncturing step and the saiddecoding procedure comprises at least one corresponding depuncturingstep.

[0057] The characteristics of the invention mentioned above, as well asothers, will emerge more clearly from a reading of the followingdescription of an example embodiment, the said description being givenin relation to the accompanying drawings, amongst which:

[0058]FIG. 1 is a diagram illustrating a coding device with a turbocodeof the two-dimensional PCCC type;

[0059]FIG. 2 is a diagram illustrating a decoding device in serial modeassociated with the coding device of FIG. 1;

[0060]FIG. 3 is a graph showing, as a function of the signal to noiseratio, the mean of the absolute value of the extrinsic informationcalculated at the output of a last decoder of a last iteration, on theone hand for correctly decoded sequences, and con the other hand forsequences exhibiting residual errors;

[0061]FIG. 4 is a flow diagram illustrating a basic principle of adecoding procedure with interrupt criterion according to one embodimentof the present invention.

[0062] The present invention will be illustrated notably with referenceto a transmission method of the error correcting coding type using aturbocode of the two-dimensional PCCC type, a turbocoding deviceapplying this method being depicted schematically in FIG. 1, and aturbodecoding device applying this method being depicted in FIG. 2. Theinvention can easily be extended to turbocodes of greater dimension,using other types of elementary codes, and/or to different concatenationschemes, notably to serial concatenation schemes, as well as todifferent turbodecoding concatenation schemes.

[0063] Overall, a digital transmission method of the error correctingcoding type by PCCC turbocode comprises a coding procedure before atransmission step and a decoding procedure after a transmission step.

[0064] The coding procedure is illustrated through the coding devicedepicted schematically in FIG. 1.

[0065] Overall, this coding device 10 comprises two elementary coders 11and 12 between which there acts an interleaver of size N 13.

[0066] Each of the elementary coders 11 and 12 is a coder using arecursive systematic convolutional (RSC) code. As is well known, each ofthese elementary coders uses a series of auxiliary information items,stored in a device of the shift register type, each obtained by themathematical combination of a useful information item and auxiliaryinformation items calculated previously. In the example presented here,the shift register 23 stores the auxiliary data calculated by theexclusive OR 21 whose inputs give the first generator polynomial of theRSC coder 11. The convolution product is produced by the exclusive OR22, the outputs of the register 23 give the second generator polynomialof the RSC coder 11. The useful information item is systematicallytransmitted alongside a redundant information item which appears at theoutput of the exclusive OR operator 22. The interleaving step 13 of sizeN modifies the order in which the data are taken into account by each ofthe elementary codes. In this way, each of the coders 11 and 12generates a redundant information item which is associated with it. Theuseful information item is transmitted only once. Thus the codedinformation item as it appears from the coding procedure is a block 20comprising the useful information item, or systematic part, and the tworedundant information items, or parts of the coded information itemcorresponding to each of the elementary codes. Naturally, the twoelementary codes could be different. After multiplexing 14, the codedinformation can be subjected to puncturing 15. The efficiency of each ofthe elementary coders is ½ and, because the systematic part istransmitted only once, the efficiency R of the turbocode is ⅓. Thisefficiency can of course be increased by puncturing. Thus the puncturingof half of the redundant bits of each elementary code would produce anefficiency R of ½.

[0067] The coded information is in the form of sequences of N blocks 20composed of the systematic information item X and the first and secondredundant items Y1 and Y2. After any puncturing, a sequence istransmitted and undergoes the modifications afforded by the channel. Itis then received by the decoding device and possibly depunctured. Thereare then N blocks 30 of length 3 at the input of the demultiplexer 31.Each of these blocks 30 constitutes a received information item to bedecoded They contain a received information part corresponding to theuseful information item, referred to as the systematic information itemX, a first received information part corresponding to the redundantinformation of the first elementary code, referred to as the firstredundant information item Y1, and a second received information partcorresponding to the redundant information item of the second elementarycode, referred to as the second redundant information item Y2. Thedecoding procedure functions by decoding sequences of N bitscorresponding to the sequences of N blocks received.

[0068] The decoding device, with serial concatenation, comprises anelementary decoder 32 corresponding to the first elementary coder 11 andan elementary decoder 33 corresponding to the second elementary coder12. In the example considered here, the elementary decoders, using analgorithm of the LogMAP type, have weighted inputs and outputs in theform of log likelihood ratios (LLRs). Because of this, the extrinsicinformation is initialised to 0 and the extrinsic information iscombined with the systematic information by addition. Naturally, if thequantities manipulated by the elementary decoders are others, it will benecessary to make the corresponding changes. For example, if it is acase of likelihood ratios, the extrinsic information is initialised to 1and the combination is effected by product. If it is a case ofprobabilities, the extrinsic information is initialised to 0.5 and thecombination is also effected by product.

[0069] On the one hand, the received information part X corresponding tothe useful information is transmitted to the elementary decoders 32 and33. In the direction of the elementary decoder 32 an adder 37 adds tothis systematic information X an extrinsic information item e2 _(k′−1).In the direction of the elementary decoder 33, an adder 39 adds to thissystematic information X, interleaved by an interleaver 34 of size Ncorresponding to the interleaver 13, an extrinsic information item e1_(k′), interleaved by an interleaver 35 of size N corresponding to theinterleaver 13. Moreover, the received information part Y1 correspondingto the redundant information of the first elementary code is transmittedto the decoder 32 and the received information part Y2 corresponding tothe redundant information of the second elementary code is transmittedto the decoder 33.

[0070] The index k′ represents the current iteration of the decodingprocedure, the extrinsic information item e2 _(k′−1) being thereforecalculated during an iteration preceding the one during which theextrinsic information item e1 _(k′) is calculated.

[0071] The extrinsic information e1 _(k′) is obtained at the output ofthe elementary decoder 32 during an iteration k′, with subtraction, at asubtractor 38, of the systematic information X and the extrinsicinformation e2 _(k′−1).

[0072] The extrinsic information e2 _(k′), is obtained, in interleavedform e′2 _(k′), at the output of the elementary decoder 33 during aniteration k′, with subtraction, at a subtractor 40, of the interleavedsystematic information X′ and the interleaved extrinsic information e′1_(k′). It is deinterleaved by a deinterleaver 36 of size N correspondingto the interleaver 13 before transmission at the following iteration.

[0073] At the end of a decoding procedure, a decoding sequence at theoutput of the second elementary decoder 33 is deinterleaved and analysedby a decision unit 41 in order to form a decoded sequence.

[0074] At the start, the extrinsic information e2 ₀ is initialised to 0.During the first iteration, the systematic information X forms the apriori input information of the first elementary decoder 32. The firstelementary decoding, as from the first redundant information item Y1,produces a weighted output information item D1 ₁, corresponding to afirst decoding sequence estimation, and written in the form of acombination of the systematic information and the extrinsic informatione1 ₁, the latter corresponding to an increase in the reliabilityassociated with the first elementary decoding. D1 ₁=X+e1 ₁, theextrinsic information e1 ₁ being written as the difference between theweighted output information of the first decoder, here the output loglikelihood ratio, and the weighted input information of the firstdecoder, here the input log likelihood ratio. This extrinsic informatione1 ₁, interleaved and added to the interleaved systematic informationX′, forms the a priori input information of the second elementarydecoder 33. The second elementary decoding, from the second redundantinformation item Y2, produces a weighted output information item D′2 ₁,which corresponds to a second decoding sequence estimation, and which iswritten in the form of a combination of the interleaved systematicinformation, the interleaved extrinsic information e′1 ₁ and theinterleaved extrinsic information e′2 ₁, the latter corresponding to anincrease in the reliability associated with the second elementarydecoding. D′2 ₁=X′+e′1 ₁+e′2 ₁, the interleaved extrinsic informatione′2 ₁ being written as the difference between the weighted outputinformation of the second decoder, here the output log likelihood ratio,and the weighted input information of the second decoder, here the inputlog likelihood ratio. The interleaved extrinsic information e′2 ₁ forms,after deinterleaving, the extrinsic information e2 ₁ which, added to thesystematic information X, forms the input a priori information of thefirst elementary decoder 32 for the second iteration. The elementarydecoding, still from the first redundant information item Y1, thenproduces a weighted output information item D1 ₂, which corresponds to anew decoding sequence estimation of increased reliability. A newextrinsic information item associated with the decoder 32 e1 ₂,interleaved and added to the interleaved systematic information X′,forms the a priori input information of the second elementary decoder33. The second elementary decoding, still from the second redundantinformation item Y2, produces a weighted output information item D′2 ₂,which corresponds to yet another new decoding sequence estimation ofincreased reliability. A new extrinsic information item associated withthe decoder 33 e2 ₂, added to the systematic information X, forms the apriori input information of the first elementary decoder 32 for thethird iteration. The process then continues in the same way, theextrinsic information, as the iterations progress, gaining inreliability, that is to say in amplitude in the present case where it isexpressed in terms of likelihood ratio logarithm. At the end of thedecoding procedure, after a number of iterations k whose determinationwill be explained below, the interleaved decoding sequence composed ofthe weighted output information items D′2 _(k) at the output of thesecond elementary decoder 33 is deinterleaved and thresholded in orderto produce the decoded sequence.

[0075]FIG. 4 depicts an embodiment of the present invention applied tothe case of an i-dimensional PCCC such as the two-dimensional PCCC whichhas just been described.

[0076] Overall, according to the invention, a characteristic quantitydetermination step 51 and a comparison step 53 adapted to compare thecharacteristic quantity with a threshold quantity are associated witheach of the elementary decoding steps 50 of an iterative decodingprocedure. The threshold quantity is determined by a threshold quantitydetermination step 52. During the elementary decoding step 50, thecharacteristic quantity determination step is adapted to calculate acharacteristic quantity of the sequence of N extrinsic information itemsat the output of the elementary decoding step 50. An interrupt step 54will interrupt the decoding procedure if the characteristic quantityreaches and exceeds the threshold quantity. If not, through the step 55,the decoding procedure will continue to the following elementarydecoding step.

[0077] More precisely, the characteristic quantity determination step 51executes an algorithm consisting, during an i′^(th) step of elementarydecoding of a k′^(th) iteration, of calculating the mean E|ei′_(k′)| ofthe absolute value of the extrinsic information calculated on thesequence of N extrinsic values at the output of the i′^(th) decoderduring the k′^(th) iteration. Advantageously, this characteristicquantity is determined for each elementary decoding step so that theiterative decoding method can be interrupted including at an elementarydecoding step situated in the body of the iteration. Alternatively, thischaracteristic quantity may be calculated only for certain elementarydecoding steps, for example for the last elementary decoding step ineach iteration.

[0078] Thus, in the case of the 2-dimensional PCCC described, thischaracteristic quantity determination step 51 determines, for example,during the elementary decoding effected by the second decoder 33 duringa k′^(th) iteration, the mean E|e2 _(k′)| of the absolute value of theextrinsic information calculated on the sequence of N extrinsic valuesand the output of the second decoder 33 during this k′^(th) iteration.

[0079] Once the characteristic quantity E|ei′_(k′)| has been determined,at the end of the i′^(th) elementary decoding step of the k′^(th)iteration, the comparison step 53 receives on the one hand thischaracteristic quantity E|ei′_(k′)| and on the other hand a thresholdquantity s determined by the threshold quantity determination step 52.If the step 53 determines that E|ei′_(k′)|>s, step 54 is executed andthe iterative decoding procedure is interrupted at the elementarydecoding step i′ of the iteration k′. In this case, the sequence of Nweighted output information items associated with the sequence of Ninformation items decoded by the decoding procedure is the sequence of Nweighted output information items generated by the i′^(th) elementarydecoder during the k′^(th) iteration. If step 53 determines thatE|ei′_(k′)| is not greater than s, step 55 is executed and the iterativedecoding procedure continues, the interrupt test then being applied atthe end of the following elementary decoding step, and so on.

[0080] The threshold quantity determination step 52 determines athreshold quantity s as a function of configuration parameters. It maybe case of parameters characterising the transmission conditions suchas, for example, the signal to noise ratio. It may also be a case ofparameters characterising, for example, the size of the usefulinformation block, an elementary decoding algorithm, a type of quantityused, a maximum number of iterations, a type of transmission channel,etc. These configuration parameters characterise the current decodingoperation.

[0081] The choice of the threshold quantity will also depend on theapplication in the context of which the numerical transmission methodacts. Thus the threshold value will often have to be chosen so as toeffect a compromise between the performance permitted by the decodingprocedure and the complexity of this decoding procedure. In the sameway, it may be chosen as a function of a mean transmission time requiredor as a function of a mean energy consumption acceptable.

[0082] In the present example embodiment, a maximum tolerable number ofiterations having been predefined, the threshold s is fixed by combiningtwo quantities calculated in the same way as the characteristic quantityaccording to the present invention is calculated, that is to say, in thepresent case, by taking the mean of the amplitudes of N extrinsicinformation items of a decoding sequence. These two quantities arepeculiar to a given configuration as defined by the configurationparameters and corresponding to the current decoding operation. Thefirst and second quantities characterise, in this given configuration, aset of extrinsic information items generated by a last elementarydecoder, at the end of the decoding procedure which executed the maximumpredefined number of iterations, respectively in the case of a decodingwithout error and in the case of a decoding for which errors remain.

[0083] Advantageously, these first and second quantities are obtained asa function of the configuration parameters by means of an adaptivealgorithm or a pre-established reference table, based on a prior studyof the evolution of the characteristic quantity according to theinvention, here the mean of the amplitudes of N extrinsic informationitems of a decoding sequence, as a unction of the configurationparameters.

[0084] By way of example, FIG. 3 shows, in the form of a graph, a resultof such a study for the PCCC of the present embodiment. The two curves61 and 60 give the mean E|e2 ₂₀| of the absolute value of the extrinsicinformation and the output of the 2^(nd) decoder of the 20^(th)iteration as a function of the signal to noise ratio Eb/No, respectivelyin the case of badly decoded sequences, that is to say those which stillcontain errors, and in the case of correctly decoded sequences, that isto say ones which contain no residual error. The values E|e2 ₂₀| havebeen calculated, in both cases and for each signal to noise ratio value,for sufficient sequences to obtain usable curves. In the presentexample, the length of the decoding sequence (corresponding to the sizeof the interleavers) is N=640. The signal at the output of theturbocoder is moderated by a BPSK modulation and transmitted over awhite additive Gaussian noise (WAGN) channel.

[0085] The curves obtained, used for example by means of a referencetable, make it possible, for a given signal to noise ratio, forming aconfiguration parameter, to deduce the first and second quantities,combining which gives the threshold quantity s.

[0086] For example, for a signal to noise ratio of 0.78 dB and a maximumnumber of iterations fixed at 20, the first quantity, characterising adecoding without error, is equal to 37.5 (point 63) and the secondquantity, characterising a decoding with residual errors, is equal to 3(point 62).

[0087] Naturally, the threshold quantity determination step can be basedon a plurality of characteristic curves, such as those depicted in FIG.3, corresponding to a plurality of configuration parameters.

[0088] In order to be able to adapt the threshold quantity with a view,for example, to making a compromise between the performance permitted bythe decoding procedure and the complexity of this decoding procedure, oras a function, for example, of a required mean transmission time, or anacceptable mean energy consumption, the determination of the thresholdquantity by combining a first quantity, characterising a decodingwithout error, and a second quantity, characterising a decoding withresidual errors, is effected by means of a coefficient a making itpossible to favour one or other of these quantities.

[0089] In the present example embodiment, the threshold quantity is thesum of the first quantity multiplied by a coefficient α and of thesecond quantity multiplied by a coefficient (1-α), the coefficient αbeing chosen between 0 and 1.

[0090] The coefficient α is determined, for example by means of anadaptive algorithm or a reference table, as a function of theapplication in the context of which the digital transmission methodacts. The smaller α is, the lower are the mean complexity of thedecoding, the mean decoding time and the mean energy consumption for thedecoding of a sequence. The larger α is, the more improved are theperformances permitted by the decoding. Thus, for example, forapplications able to tolerate relatively high binary or packet errorrates but requiring low transmission times, as is the case with voiceservices, the parameter α is rather chosen so as to be small. For suchapplications, the maximum number of iterations is also small. On theother hand, for applications requiring low binary or packet error ratesbut tolerating high transmission times, as is the case with datatransfer services, the parameter a and the maximum number of iterationsare rather chosen so as to be great.

[0091] For example, in the example of FIG. 3, for a signal to noiseratio of 0.78 dB, a coefficient α equal to 0.35 gives a thresholdquantity s equal to 15. If a procedure for the iterative decoding of asequence is interrupted when the characteristic quantity calculated forthis sequence attains the threshold quantity s=15, the performance interms of bit error rates is not or is only slightly degraded comparedwith the case where the decoding procedure goes to the end of its twentyiterations. On the other hand, the mean number of iterations effected is3.8 instead of 20, which results in a saving in complexity greater than5.

[0092] The present invention applies to all types of transmission methodusing an error correcting code of the turbocoding type, whether it is acase of a serial or parallel turbocoding, or even a turbocode with ahybrid concatenation scheme mixing serial concatenation and parallelconcatenation.

[0093] One embodiment of the present invention applied to a serialturbocode will be presented briefly.

[0094] For example, in a serial concatenation turbocode, each elementarycoder generates an elementary coded information item from the elementarycoded information item issuing from the previous elementary coders, thei elementary coders being separated by (i−1) interleavers. Puncturingsteps can be distributed in the coding procedure, the output of a j^(th)coder being able to be punctured by a j^(th) puncturing vector,interleaved by a j^(th) interleaver before coding by a (j+1)^(th) coder.The size of each interleaver depends on the previous coding step and, inparticular, on the efficiency after puncturing of the previouselementary coder.

[0095] In an example of turbodecoding corresponding to the serialconcatenation turbocoding which has just been described, the elementarydecoders being associated in the reverse order of the elementary coders,each elementary decoding step receives two a priori weighted informationitems, one, referred to as the first input information item,corresponding to the output information item of the correspondingelementary coder, and the other, referred to as the second inputinformation item, corresponding to the input information item of thecorresponding elementary coder. This elementary decoding step producestwo a posteriori weighted information items, one, referred to as thefirst output information item, corresponding to the output of thecorresponding elementary coder, and which therefore becomes, during afollowing iteration, after interleaving and corresponding puncturing,the a priori input of a previous elementary decoder, and the other,referred to as the second output information item, corresponding to theinput of the corresponding elementary coder, and which thereforebecomes, in the same iteration, after deinterleaving and correspondingdepuncturing, the a priori input of a following elementary decoder. Thefirst input information item corresponds to the information to bedecoded by the elementary decoding step. The second output informationcorresponds to the information decoded by the elementary decoding step,and consists of the combination of the second input information item andan extrinsic information item.

[0096] According to the present invention, the characteristic quantitydetermination step calculates, during an elementary decoding step, acharacteristic quantity from a set of extrinsic information items at theoutput of this elementary decoding step. For example, if reference ismade to the previously described turbodecoding example, thecharacteristic quantity calculation is made using a set of extrinsicinformation items issuing from a set of second output information items.

1. digital transmission method of the type with error correcting coding,comprising, before a step of transmission over a channel, a codingprocedure for generating, from a useful information item, a codedinformation item comprising at least one redundant information item and,after the said step of transmission over the said channel, a decodingprocedure in order to obtain, from a received information item to bedecoded, an estimation of said useful information item with correctionof the transmission errors based on said at least one redundantinformation item, said coding procedure comprising a plurality ofelementary coding steps associated with at least one interleaving stepand operating in parallel or in series, said decoding procedure beingiterative and comprising, for each iteration, a plurality of elementarydecoding steps associated with interleaving and deinterleaving steps,corresponding to said plurality of elementary coding steps associatedwith said at least one interleaving step, each of said elementarydecoding steps (50) receiving a set of information to be decoded andgenerating a set of weighted output information items associated with aset of decoded information, the said method being characterised in thatit comprises a step of determining a characteristic quantity (51)adapted to calculate, for each of said elementary decoding steps (50), aquantity characteristic of the said set of weighted output informationitems, a comparison step (53) adapted to compare the said characteristicquantity with a threshold quantity, and an interrupt step (54) forinterrupting said decoding procedure when said characteristic qualityreaches the said threshold quantity.
 2. Digital transmission method ofthe error correcting coding type according to claim 1, characterised inthat, each of said elementary decoding steps (50) generating a set ofextrinsic information items corresponding to the said set of weightedoutput information items, the said characteristic quantity determinationstep (51) is adapted to calculate, for each of the said elementarydecoding steps (50), a quantity characteristic of the said set ofextrinsic information items.
 3. Digital transmission method of the errorcorrecting coding type according to claims 1 or 2, characterised in thatthe said characteristic quantity calculated by the said characteristicquantity determination step (51) is a statistical quantitycharacterising the said set of weighted output information items. 4.Digital transmission method of the error correcting coding typeaccording to claim 3, characterised in that the said characteristicquantity calculated by the said characteristic quantity determinationstep (51) is the mean of the absolute value of the weighted outputinformation item calculated on the said set of weighted outputinformation items.
 5. Digital transmission method of the errorcorrecting coding type according to claim 3 or 4, characterised in thatthe said interrupt step (54) interrupts the said decoding procedure whenthe said characteristic quantity is greater than the said adaptedthreshold quantity.
 6. Digital transmission method of the errorcorrecting coding type according to any one of the preceding claims,characterised in that the said digital transmission method alsocomprises a threshold quantity determination step (52) for determining athreshold quantity as a function of at least one configurationparameter.
 7. Digital transmission method of the error correcting codingtype according to claim 6, characterised in that configurationparameters are the signal to noise ratio, the size of the usefulinformation block, the elementary decoding algorithm, the type ofquantity used, the maximum number of iterations and the type oftransmission channel.
 8. Digital transmission method of the errorcorrecting coding type according to claim 6 or 7, characterised in thatthe said threshold quantity determination step (52) uses an adaptivealgorithm making it possible to calculate the said threshold quantity asa function of one or more configuration parameters.
 9. Digitaltransmission method of the error correcting coding type according toclaim 6 or 7, characterised in that the said threshold quantitydetermination step (52) uses a pre-established reference table making itpossible to select the said threshold quantity as a function of one ormore configuration parameters.
 10. Digital transmission method of theerror correcting coding type according to any one of claims 6 to 9,characterised in that the said threshold quantity determination step(52) determines a threshold quantity so as to make a compromise betweenthe performance permitted by the said decoding procedure and thecomplexity of this decoding procedure.
 11. Digital transmission methodof the error correcting coding type according to any one of claims 6 to9, characterised in that the said threshold quantity determination step(52) determines a threshold quantity as a function of a required meantransmission time.
 12. Digital transmission method of the errorcorrecting coding type according to any one of claims 6 to 9,characterised in that the said threshold quantity determination step(52) determines a threshold quantity as a function of an acceptable meanenergy consumption.
 13. Digital transmission method of the errorcorrecting coding type according to any one of claims 6 to 12,characterised in that, a tolerable maximum number of iterations havingbeen predefined, the said threshold quantity determination step (52)determines a threshold quantity by combining on the one hand a firstquantity (63) characteristic of a first set of weighted outputinformation items generated by a last elementary decoder during a lastiteration and associated with a first set of decoded information itemscorresponding to the error-free decoding of a set of information itemsto be decoded, and on the other hand a second quantity (62)characteristic of a second set of weighted output information itemsgenerated by the said last decoder during the said last iteration andassociated with a second set of decoded information items correspondingto the decoding of the said set of information items to be decoded inthe case where errors remain.
 14. Digital transmission method of theerror correcting coding type according to claim 13, characterised inthat the said first and second quantities (63, 62) are statisticalquantities characteristic respectively of the said first set of weightedoutput information items and of the said second set of weighted outputinformation items.
 15. Digital transmission method of the errorcorrecting coding type according to claim 13, characterised in that thesaid first and second quantities (63, 62) are the means of the absolutevalue of the weighted output information item calculated on,respectively, the said first set of weighted output information itemsand the second set of weighted output information items.
 16. Digitaltransmission method of the error correcting coding type according to anyone of claims 13 to 15, characterised in that the said first and secondquantities (63, 62) are determined, as a function of at least oneconfiguration parameter, by means of an adaptive algorithm.
 17. Digitaltransmission method of the error correcting coding type according to anyone of claims 13 to 15, characterised in that the said first and secondquantities (63, 62) are determined, as a function of at least oneconfiguration parameter, by means of an adaptive algorithm.
 18. Digitaltransmission method of the error correcting coding type according to anyone of claims 13 to 15, characterised in that the said first and secondquantities (63, 62) are determined, as a function of at least oneconfiguration parameter, by means of a pre-established reference table.19. Digital transmission method of the error correcting coding typeaccording to any one of claims 13 to 17, characterised in that the saidthreshold quantity is the sum of the said first quantity (63) multipliedby a coefficient α and of the said second quantity (62) multiplied by acoefficient (1-α), the coefficient α being chosen between 0 and
 1. 20.Digital transmission method of the error correcting coding typeaccording to claim 19, characterised in that the said coefficient α ischosen so as to effect a compromise between the performance permitted bythe said decoding procedure and the complexity of this decodingprocedure.
 21. Digital transmission method of the error correctingcoding type according to claim 19, characterised in that the saidcoefficient α is chosen as a function of a required mean transmissiontime.
 22. Digital transmission method of the error correcting codingtype according to claim 19, characterised in that the said coefficient αis chosen as a function of an acceptable mean energy consumption. 23.Digital transmission method of the error correcting coding typeaccording to any one of claims 19 to 22, characterised in that the saidcoefficient α is determined by means of an adaptive algorithm. 24.Digital transmission method of the error correcting coding typeaccording to any one of claims 19 to 22, characterised in that the saidcoefficient α is determined by means of a pre-established referencetable.
 25. Digital transmission method of the error correcting codingtype according to any one of the preceding claims, characterised in thatthe said elementary decoding steps (50) have inputs and outputs whichare weighted, in terms of probabilities, likelihood ratios or loglikelihood ratios.
 26. Digital transmission method of the errorcorrecting coding type according to any one of the preceding claims,characterised in that the said coding procedure comprises at least onepuncturing step and the said decoding procedure comprises at least onecorresponding depuncturing step.